So Kylo Ren said he'd finsh what Vader had started..that makes me wonder what it is that Vader had started but did not finish. And I can only conclude one thing.
Vader never had his chance to be Luke and Leia's father.
I am saying Kylo just want to have play time with old Luke and Leia, be their father figure and gives his approval of Leia dating Han
But someone just have to mess it up.